Thévenin's Theorem

Thévenin's Theorem

In this lab project we examine series-parallel circuit in order to determine the current in one specific branch of the examined circuit (usually load current). DC Power Supply supplies the circuit with time-constant electromotive force. Analyzes will be provided by Thevenin's Theorem. The purpose of the project is to verify the theory of Thevenin's Theorem.

Theory Part 1

Thevenin's Theorem

Thevenin's Theorem can be demonstrated using the circuit shown in Figure 1. In Figure 1 is shown circuit with four resistors

and RL,

connected with voltage generator with electromotive force E=20 V. The assignment is to determine current IL trough resistor RL.

The calculation of the expected current trough and the voltage across the resistorRL can be simplified by using Thevenin's Theorem. If the entire circuit with the exception of terminals A and B were enclosed in a "black box", then it may be replaced by the circuit shown in Figure 2 using the equivalent Thevenin voltageET in series with the equivalent Thevenin resistance RT .

If these Thevenin equivalent values are known, the expected current through, and the voltage across RL may be calculated easily by using Ohm's Law. The Thevenin voltage, ET, appears the unloaded terminals A and B. Since no current flow throughR3 in Figure 2 when A and B are unloaded, the voltage appearing across terminals A and B is the same as the voltage appearing across R2. Therefore ET=ER2. Assume a 20 V dc input and calculate the Thevenin voltage ET across terminals A and B.

Now, calculate the Thevenin equivalent resistance RT, appearing across terminals A and B. Assume that a direct short replaces the 20 V dc power source. Therefore, R1, is now in parallel with R2. Their equivalent parallel resistance in series withR3, is the Thevenin resistance RT.

In Figure 3 are shown two identical circuit (The circuit from Figure 1 and the equivalent Thevenin circuit)

Calculate the current IL through resistance RL using Thevenin equivalent valuesET and RT.

Practice Part 1

Equipment:

Breadboard

DC Power Supply with time-constant EMF (0 to 25.0V DC)

Three resistors with: and one variable resistor,

Two universal instruments.

Procedure: Connect the circuit as it shown in Figure 4.

Experimental determination of equivalent Thevenin generator

1) Disconnect the ammeter and variable resistance RL. Set up the voltage on 20 V.

2) Connect the voltmeter between terminals A and B and measure the Thevenin voltage generator

3) Connect the ammeter and measure the current of short circuit between terminals A and B with (RL=0)

4) Calculate the equivalent resistance ( RL=0 – short circuit on terminals A and B).

Experimental determination of the current IL and the power PL for the resistor RL

5) Connect again the circuit shown in Figure 4. Set up and keep the voltage at 20V. Changing the resistance of the variable resistor RL for the values in Table 1 measure and record the values of current IL through resistor RL and the voltage UL across the resistor RL.

Table 1

Measured

Measured

Calculated

ResistanceRl (k?)

CurrentIl (mA)

Voltage(V)Ul=Rl Il

Power (W)

Pl= Ul Il

0

2

4

6

8

RT

?

6) From the data in Table 1 draw graphs for the UL=f (IL) and PL=f (RL)

and one variable resistor

Two universal instruments

Procedure:

7) In Figure 5 is shown equivalent Thevenin circuit. Connect the component of the circuit and set the voltage of the source at the equivalent Thevenin voltageET calculated in Theory Part 1.

8) Connect one of the multimeters as a voltmeter across the source and the other as ammeter between the resistors R4=RT and RL.

9) Changing the resistance of the resistor RL for the values in Table 2 measure and record the values of currentIL through resistor RL and the voltage UL across the resistorRL.

10) Calculate and record the power on the resistor RL for the values from Table 2.

Table 2

Measured

Measured

Calculated

ResistanceRl (k?)

CurrentIl (mA)

Voltage(V)Ul=Rl Il

Power (W)Pl= Ul Il

0

2

4

6

8

RT

?

11) From the data in Table 2 draw graph for the UL=f (IL) and PL=f (RL).